A roof rises 9.75 ft over a horizontal distance of 15.84ft. What is the slope of the roof to the nearest hundredth?

I am not sure if i am using the right fomula.

i used the slope

rise/run

therefore i got : 0.6155303

and when rounded to the hundreadths place

i get 0.62

is the formula correct

and how can i check this ?

This looks fine to me

The roof of a house rises 5 feet over a horizontal distance of 15 feet

Yes, your formula and calculation for the slope of the roof are correct. The formula to calculate slope is rise divided by run, which is essentially the vertical distance divided by the horizontal distance. In this case, the rise of the roof is 9.75 ft and the run is 15.84 ft, so you correctly calculated the slope as 0.6155303.

To confirm the accuracy of your calculation, you can use a slope triangle diagram to visualize the rise and run. Draw a right triangle with one side representing the rise (9.75 ft) and the other side representing the run (15.84 ft). Then, calculate the angle that the roof makes with the horizontal by taking the inverse tangent of the slope. If the angle matches your expectations based on the given rise and run, it confirms that your slope calculation is correct.

In this case, the inverse tangent of 0.6155303 is approximately 31.32 degrees. So, the roof makes an angle of about 31.32 degrees with the horizontal, which you can verify using a protractor or measuring device. If the calculated angle matches the actual angle of the roof as observed, it further indicates that your slope calculation is accurate.